ISSN 2307–3489 (Print), ІSSN 2307–6666 (Online)

Наука та прогрес транспорту. Вісник Дніпропетровського
національного університету залізничного транспорту, 2016, № 6 (66)

інформаційно-комунікаційні технології та математичне моделювання

Introduction

To make a forecast of the network traffic parameters there are used various methods and techniques that are widely spread in the analysis of time series of economic indicators [9-10]. In general, if the set of discrete values at successive time points , then the forecasting problem lies in forecasting the value at a future time point . The forecast usually has an error, but this error depends on the used forecasting system. High efficiency of the forecast is achieved with the use of neural networks [1, 11-13]. The forecasting problem can be solved based on the following neural networks: multilayer perceptron (MLP), radial basis function (RBF), generalized regression neural network (GRNN), Volterra networks, Elman networks and ANFIS-system, the overview of which is done in [7]. Fuzzy Neural Networks (hybrid systems) are designed to combine the advantages of neural networks and fuzzy inference. They allow you to develop and apply the models in the form of the rules of fuzzy production systems, for the building of which the neural network capabilities are used [5]. In particular, the adaptive network of fuzzy inference (Adaptive-Network-Based Fuzzy Inference System, ANFIS), which is implemented in the Fuzzy Logic Toolbox application of Matlab program [4]. The main stages of neuro-fuzzy network operation include: formation of the rule base of fuzzy inference system; phasing of input variables; aggregation; activation; accumulation; defuzzification of output variables, the functioning algorithm of such a system is provided in [6]. Specifically, [2] proposed a hybrid forecasting system (24 hours ahead) for the suburban passenger flow and [3] formed a hybrid model for forecasting the wagon loading volume for two previous days.

Purpose

To develop the method for forecasting the volume of network traffic (incoming and outgoing) through the use of neuro-fuzzy network (hybrid system) for the considered fragment (Dnipropetrovsk-Kyiv) in ITS of Prydniprovsk railway.

Problem statement

Continuous increase in network traffic volume in ITS of Prydniprovsk Railways requires its forecasting to prevent network congestion and improve service quality. One of the possible solutions can be the network traffic volume forecasting method that would avoid such an overload (including that of the server). The study used the real traffic data of the most important fragment (Dnipropetrovsk – Kyiv) in ITS of Prydniprovsk Railways for the period 21.03-26.03.2016. The analysis of inbound and outbound traffic in the direction of finding long-term dependency (hours, days) was conducted. For illustrative purposes we built the charts of network traffic volume for the analyzed ITS fragment. As an example, Figure 1 shows outbound traffic for fragment length of 24-hour time series on different days of the week.

Figure 1 shows the trend of behaviour of the network traffic volume for the week: it is about the same on Monday, Tuesday, Thursday and Friday; there are regular changes in a given period. So, in particular, the traffic volume is lower and more or less stable from 00:00 to 7:00, significant and unstable traffic from 8:00 to 17:00, and again the lower and relatively unchanged traffic from 18:00 to 23:00. On Wednesday the volume of network traffic is the highest, and on weekends the traffic volume is much lower than on weekdays. The figure shows that the volume of outbound traffic on Wednesday as compared to Monday, Tuesday, Thursday and Friday is about 1.3 times higher. To make a (day ahead) forecast of the network traffic volume we selected the interval from 8:00 to 17:00, where it has significant variations, but for weekdays (Monday, Tuesday, Thursday, Friday) when the nature of traffic is approximately the same. Thus it was decided to make a (day ahead) forecast of the traffic volume x(t) based on the data of the previous three days: x(t-1), x(t-2), x(t-3).

Fig. 1. Volume of outbound traffic in ITS (Dnipropetrovsk – Kyiv)

Methodology

1 – Preparation of sets. To make a forecast it is necessary to prepare the following sets: learning, test, validation ones. The prepared set will affect the efficiency of learning and testing processes, as well as the ability of the network to solve the problems it faces during operation. To prepare the set we made a special array of 100 examples close to reality. To form the learning set the first 50 values of the created array were used while the other 50 values were used for the test set. To form a control set we used the real data of the fourth day, which is not considered.

2 – Creation of neuro-fuzzy network in Matlab. The task of forecasting the traffic (inbound, outbound) at the section Dnipropetrovsk-Kyiv is reduced to the problem of time series forecasting, usually for such problems there is selected Sugeno type system. For the purposes of linguistic assessment each input variable has two terms (maximum and minimum value), the membership function is chosen as Gaussian (gaussmf), for assessing the resulting variable the set membership function is of linear type. In the knowledge-base editor the set fuzzy inference rules are as follows:

if x(t-1)=min and x(t-2)=min and x(t-3)=min,

then x(t)=1;

if x(t-1)=min and x(t-2)=min and x(t-3)=max,

then x(t)=2;

if x(t-1)=min and x(t-2)=max and x(t-3)=min,

then x(t)=3;

if x(t-1)=min and x(t-2)=max and x(t-3)=max,

then x(t)=4;

if x(t-1)=max and x(t-2)=min and x(t-3)=min,

then x(t)=5;

if x(t-1)=max and x(t-2)=min and x(t-3)=max,

then x(t)=6;

if x(t-1)=max and x(t-2)=max and x(t-3)=min,

then x(t)=7;

if x(t-1)=max and x(t-2)=max and x(t-3)=max,

then x(t)=8.

The structure of the designed fuzzy inference system is shown in Fig. 3.

Fig. 2. Membership function of the first input variable before and after system learning

Fig. 3. Structure of the designed hybrid system

As shown in Fig. 3, the system has 5 layers. The first layer (input) – has three nodes (х(t–3), х(t–2), х(t–1)), where the input data are conveyed. The first layer performs dividing phasing of each variable, defining for each -th rule of inference of the membership coefficient according to the applicable phasing function. The second layer (inputmf) consists of nodes, because each input variable corresponds to 2 terms, performs aggregation of individual variables , determining the resulting value of the membership coefficient for vector (the activation level of inference rule); this layer is nonparametric. The third layer (rule) is TSK function generator; this is a parametric layer which involves adaptation of the linear weight determining the function of TSK model inference. The fourth layer (outputmf) consists of membership functions for each fuzzy inference rule (number of nodes of this layer corresponds to the number of rules 2³ = 8); this layer is nonparametric. The fifth layer (output) is normalizing, it has a single node, which corresponds to the output of the system; this layer is nonparametric.

3 – Learning of fuzzy neural network. When learning the hybrid method (hybrid) was selected as the method of optimization (optim. method), which combines the least-square method and the reduced reverse gradient method; the number of iterations of learning (epochs) is 40. As an example, the diagram of membership function of the first input variable before and after system learning is shown in Fig. 2.

4 – Testing of hybrid system. The hybrid system testing is conducted on the test set. Testing results as compared to the system learning results are shown in Fig. 4.

5 – Analysis of hybrid system adequacy. To assess the quality and accuracy of the forecast of the created hybrid system we calculated MAPE (Mean Absolute Percentage Error) by the formula:

(1)

where – real data at time point t; – predicted data at time point t; N – number of hours.

Forecasting of the network traffic volume was conducted from 8:00 to 17:00 (total hours N = 10). MAPE values are: 6.9% for the forecast of inbound traffic volume, 7.7% for the forecast of outbound traffic volume. As an example the actual and predicted volume of outbound traffic in ITS of Dnieper Railways (Dnipropetrovsk-Kyiv) is shown in Fig. 5.

Fig. 4. Results of learning and testing
of neuro-fuzzy network

Fig. 5. Actual and predicted volumes of outbound traffic

Findings

1 – The study of dependence of the average error of the hybrid system learning on the number of its inputs. The study involved the average error of the created hybrid system learning with different number of inputs: 2, 3, 4. In all the experiments, the length of the learning set was 50 examples, the number of epochs – 40, system learning was conducted by hybrid method. The obtained data resulted in the built diagrams of the dependence of the average error of the hybrid system learning on the number of its inputs for inbound (outbound) traffic in ITS of Prydniprovsk Railways for the considered fragment Dnipropetrovsk-Kyiv and are presented in Fig. 6.

The figure shows that lowest value of the average error of the hybrid system learning is: 0.27∙10^-3∙10⁶ = 2.7∙10² bursts for inbound traffic; for outbound traffic is provided by 4-input hybrid system at the learning set consisted of 50 examples.

2 – The study of dependence of the average error of the hybrid system learning on the number of terms of its input variable. The study was conducted on the created hybrid system, which has three input variables; in all the experiments the length of learning set consisted of 50 examples. Let us analyse the value of the average error of the hybrid system learning based on the number of terms of its input variable: 2, 3, 5.

The obtained values resulted in the built diagrams of the dependence of the average error of the hybrid system learning on the number of terms of its input variable by different learning methods that are presented in Fig. 7.

Fig. 6. Dependence of average error of the hybrid system learning
on the number of its inputs

Fig. 7. Dependence of average error of the hybrid system learning
on the number of terms of its input variable

The figure shows that when the number of terms increases (from 2 to 5), the average error of the hybrid system learning decreases: from 0.69∙10⁶ to 0.45∙10^-5∙10⁶=4.5 bursts by the hybrid learning method; from 1.36∙10⁶ to 0.83∙10⁶ bursts by the back-propagation method. Thus, learning of the 3-input hybrid system (5 terms for each input variable) is more accurate by the hybrid method than by the back-propagation method.

3. The study of dependence of the average error of the hybrid system learning on the learning set power. For the study we took the learning set of different lengths: 20, 50, 100. The study was conducted on the hybrid system with three input variables; the learning cycle was 100 epochs. The obtained values resulted in the built diagrams of the dependence of the average error of the hybrid system learning on the learning set power according to the learning algorithms that are presented in Fig. 8.

The figure shows that when the learning set power increases (20 to 100 examples) onto 3-input hybrid system, its average learning error decreases: from 0.72∙10⁶ to 0.41∙10⁶ bursts by the hybrid learning method; from 2.28∙10⁶ to 1.07∙10⁶ bursts by the back-propagation method. Thus, learning of the hybrid system is more accurate by the hybrid method at learning set power of 100 examples.

Originality and practical value

The originality of the work includes the obtained dependences for the average hybrid system error of the network traffic volume forecasting for the fragment (Dnipropetrovsk-Kyiv) in ITS of Prydniprovsk Railways on: the number of its inputs, the number of input variable terms, the learning set power for different learning methods. The practical value is that forecasting of network traffic volume in ITS of Prydniprovsk Railways will allow for real-time identification of the network congestion and control of data flows.

Conclusions

1. The work presents the conducted analysis of the volume of network traffic (inbound and outbound) in ITS of Prydniprovsk Railways (Dnipropetrovsk-Kyiv) based on the real data. For forecasting (day ahead) the volume of network traffic the interval from 8:00 to 17:00 o’clock was selected, where there are significant variations, but at that time of the week (Monday, Tuesday, Thursday, Friday) when the nature of traffic is approximately the same.

2. There were prepared the learning, test and validation sets based on actual data for the period 21.03.-26.03.2016. Forecast of the network traffic volume in ITS of Prydniprovsk Railways (Dnipropetrovsk-Kyiv) is made using a neuro-fuzzy network (hybrid system), which was designed in Matlab program. The hybrid system input is supplied with the network traffic volume for the past three days; forecasting of the network traffic volume was conducted from 8:00 to 17:00 (total hours N = 10); MAPE values are: 6.9% for inbound traffic; 7.7% for outbound traffic.

Fig. 8. Dependence of average error of the hybrid system learning on the learning set power

3. The experimental study was conducted over the dependence of the average error of the hybrid system learning on: the number of its inputs (first study), the number of input variable terms (second study), the learning set power (third study) by different learning methods: hybrid, back-propagation. Significant impact on the average error of the hybrid system learning has the number of input variable terms. In ITS of Prydniprovsk Railways (Dnipropetrovsk-Kyiv):

– The first study showed that the most accurate volume forecast of the inbound traffic (learning error 2.7∙10²) and outbound traffic (learning error 19∙10²) is achieved with 4-input hybrid system at the length of the learning set of 50 examples;

– The results of the second study showed that increase in the number of terms (from 2 to 5) of its input variable leads to decrease in the average learning error: from 0.69∙10⁶ to 4.5 bursts by the hybrid method; from 1.36∙10⁶ to 0.83∙10⁶ bursts by back-propagation method. Thus, learning of the 3-input hybrid system that has 5 terms for each input variable, is more accurate by the hybrid method;

– The results of the third study showed that increase in the learning set power (from 20 to 100 examples) onto 3-input hybrid system leads to decrease in the average learning error: from 0.72∙10⁶ to 0.41∙10⁶ bursts by the hybrid method; from 2.28∙10⁶ to 1.07∙10⁶ bursts by the back-propagation method. Thus, the learning is more accurate by the hybrid method at the learning set power of 100 examples.

LIST OF REFERENCE LINKS

1. Герасина, А. В. Адаптивное нечеткое прогнозирование трафика в информационных телекоммуникационных сетях / А. В. Герасина // Системи обробки інформації : зб. наук. пр. / Харк. ун-т повітр. сил ім. Івана Кожедуба. – Харків, 2013. – Вип. 9 (116). – С. 141–145.

2. Константінов, Д. В. Формування адаптивної технології приміських залізничних перевезень : автореф. дис. … канд. техн. наук : 05.22.01 / Константінов Денис Володимирович ; Укр. держ. акад. залізн. трансп. – Харків, 2010. – 20 с.

3. Костєнніков, О. М. Удосконалення технології формування місцевого вагонопотоку на дільниці в умовах сезонного коливання обсягів навантаження : автореф. дис. … канд. техн. наук : 05.22.01 / Костєнніков Олексій Михайлович ; Укр. держ. акад. залізн. трансп. – Харків, 2012. – 20 с.

4. Леоненков, А. В. Нечеткое моделирование в среде MatLAB и fuzzy TECH / А. В. Леоненков. – Санкт-Петербург : БХВ-Петербург, 2003. – 736 с.

5. Манусов, В. З. Краткосрочное прогнозирование электрической нагрузки на основе нечеткой нейронной сети и ее сравнение с другими методами / В. З. Манусов, Е. В. Бирюков. – Изв. Томск. политехн. ун-та. – 2006. – Т. 309, № 6. – С. 153–158.

6. Мещеряков, В. А. Моделирование адаптивной системы нейронечеткого управления рабочим процессом стрелового крана / В. А. Мещеряков, И. В. Денисов // Проектирование инженер. и науч. приложений в среде MatLAB : материалы V Междунар. науч. конф. – Харьков, 2011. – С. 367–375.

7. Пахомова, В. М. Розробка підсистеми оперативного прогнозування простоїв прибуваючих поїздів на основі ANFIS-системи / В. М. Пахомова, С. Ю. Дмітрієв // Інформ.-керуючі системи на залізн. трансп. – 2013. – № 4. – С. 46–55.

8. Пахомова, В. М. Дослідження інжинірингу трафіка в комп’ютерній мережі УЗ за технологією MPLS TE / В. М. Пахомова // Наука та прогрес транспорту. – 2015. – № 1 (55). – C. 139–147. doi: 10.15802/STP2015/38262.

9. Покровская, М. А. Метод прогнозирования изменения трафика с использованием нейросетевой модели / М. А. Покровськая // T-Comm – Телекоммуникации и Транспорт. – 2012. – № 6. – С. 27–30.

10. Сравнительный анализ методов прогнозирования трафика в телекоммуникационных системах [Electronic resource] / К. М. Руккас, Ю. В. Соляник, К. А. Овчинников, О. О. Давид // Проблемы телекоммуникаций. – 2014. – № 1 (13). – С. 84–95. – Available at: http://pt.journal.kh.ua/2014/1/1/141_rukkas_analysis.pdf. – Title from the screen. – Accessed : 22.11.16.

11. Chabaa, S. Identification and prediction of internet traffic using artificial neural networks / S. Chabaa, A. Zeroual, J. Antari // J. of Intelligent Learning Systems and Applications. – 2010. – Vol. 02. – Iss. 03. – P. 147–155. doi: 10.4236/jilsa.2010.23018.

12. Gowrishankar, S. A time series modeling and prediction of wireless network traffic / S. Gowrishankar, P. S. Satyanarayana // Intern. J. of Interactive Mobile Technologies (iJIM). – 2009. – Vol. 3. – Iss. 1. – P. 53–62. doi: 10.3991/ijim.v3i1.284.

13. Multi-scale Internet traffic forecasting using neural networks and time series methods / P. Cortez, M. Rio, M. Rocha, P. Sousa // Expert Systems. – 2010. – Vol. 29. – Iss. 2. – P. 143–155. doi: 10.1111/j.1468-0394.2010.00568.x.

В. М. ПАХОМОВА^1*

^1*Каф. «Електронні обчислювальні машини», Дніпропетровський національний університет залізничного
транспорту імені академіка В. Лазаряна, вул. Лазаряна, 2, Дніпро, Україна, 49010, тел. +38 (056) 373 15 89,
ел. пошта viknik.p1988@mail.ru, ORCID 0000-0001-8346-0405

ПРОГНОЗУВАННЯ ОБСЯГУ МЕРЕЖЕВОГО ТРАФІКа

В ІНФОРМАЦІЙНО-ТЕЛЕКОМУНІКАЦІЙНІЙ СИСТЕМІ

ПРИДНІПРОВСЬКОЇ ЗАЛІЗНИЦІ НА ОСНОВІ

НЕЙРОНЕЧІТКОЇ МЕРЕЖІ

Мета. Постійне збільшення обсягу мережного трафіка в інформаційно-телекомунікаційній системі (ІТС) Придніпровської залізниці призводить до необхідності визначення в реальному часі перевантаження в мережі та здійснення контролю потоків даних. Одним із можливих рішень є метод прогнозування обсягу мережного трафіка (вхідного та вихідного) з використанням нейромережної технології, що дозволить уникнути перевантаження сервера та підвищити якість послуг. Методика. В роботі виконані аналіз існуючого мережного трафіка в ІТС Придніпровської залізниці та підготовка вибірок: навчальної, тестової, контрольної, а також створення в програмі Matlab нейронечіткої мережі (гібридної системи) та організація на відповідних вибірках таких етапів: навчання, тестування, аналіз адекватності прогнозу. Результати. Для фрагмента (Дніпропетровськ – Київ) в ІТС Придніпровської залізниці здійснений прогноз (на добу вперед) обсягу мережного трафіка на основі гібридної системи, що створена в програмі Matlab; значення MAPE складає: 6,9 % для обсягу вхідного трафіка; 7,7 % для обсягу вихідного трафіка. Виявлено, що середня похибка навчання гібридної системи зменшується при збільшенні: кількості входів (від 2 до 4); кількості термів (від 2 до 5) вхідної змінної; потужності навчальної вибірки (від 20 до 100). Значний вплив на середню похибку навчання гібридної системи має кількість термів її вхідної змінної. Визначено, що найменше значення середньої похибки навчання надає чотири-вхідна гібридна система, більш точно здійснюється навчання нейронечіткої мережі за гібридним методом. Наукова новизна. Отримані залежності середньої похибки навчання гібридної системи прогнозування обсягу мережного трафіка фрагмента (Дніпропетровськ–Київ) в ІТС Придніпровської залізниці від: кількості її входів, кількості термів вхідної змінної, потужності навчальної вибірки за різними методами навчання. Практична значимість. Прогнозування обсягу мережного трафіка в ІТС Придніпровської залізниці дозволить в реальному часі визначити перевантаження в мережі та здійснити контроль потоків даних.

Ключові слова: прогнозування; мережний трафік; обсяг; нейронечітка мережа; гібридна система; терм; функція приналежності; вибірка; адекватність; похибка

В. Н. ПАХОМОВА^1*

^1*Каф. «Электронные вычислительные машины», Днепропетровский национальный университет
железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днипро, Украина, 49010,
тел. +38 (056) 373 15 89, эл. почта viknik.p1988@mail.ru, ORCID 0000-0001-8346-0405

ПРОГНОЗИРОВАНИЕ ОБЪЕМА СЕТЕВОГО трафИка

в ИНФОРМАЦИОННО-ТЕЛЕКОММУНИКАЦИОННОЙ

СИСТЕМЕ ПРИДНЕПРОВСКОЙ ДОРОГИ НА ОСНОВЕ

НЕЙРОНЕЧЕТКОЙ СЕТИ

Цель. Постоянное увеличение объема сетевого трафика в информационно-телекоммуникационной системе (ИТС) Приднепровской железной дороги приводит к необходимости определения в реальном времени перегрузки в сети и осуществления контроля потоков данных. Одним из возможных решений является метод прогнозирования объема сетевого трафика (входного и выходного) с использованием нейросетевой технологии, что позволит избежать перегрузки сервера и повысить качество услуг. Методика. В работе проведены анализ существующего сетевого трафика в ИТС Приднепровской железной дороги и подготовка выборок: учебной, тестовой, контрольной, а также создание в программе Matlab нейронечеткой сети (гибридной системы) и организация на соответствующих выборках следующих этапов: обучение, тестирование, анализ адекватности прогноза. Результаты. Для фрагмента (Днепропетровск–Киев) в ИТС Приднепровской железной дороги осуществлен прогноз (на сутки вперед) объема сетевого трафика на основе гибридной системы, созданной в программе Matlab; значение MAPE составляет: 6,9 % для объема входящего трафика; 7,7 % для объема выходящего трафика. Выявлено, что средняя ошибка обучения гибридной системы уменьшается при увеличении: количества входов (от 2 до 4); количества термов (от 2 до 5) входной переменной; мощности обучающей выборки (от 20 до 100), большое влияние на среднюю ошибку обучения гибридной системы оказывает число термов ее входной переменной. Определено, что наименьшее значение ошибки обучения дает 4-входная гибридная система, более точно осуществляется обучение нейронечеткой сети по гибридному методу. Научная новизна. Получены зависимости средней ошибки обучения гибридной системы прогнозирования объема сетевого трафика фрагмента (Днепропетровск – Киев) в ИТС Приднепровской дороги от: количества входов, количества термов входной переменной, мощности обучающей выборки при различных методах обучения. Практическая значимость. Прогнозирование объема сетевого трафика в ИТС Приднепровской дороги позволит в реальном времени определить перегрузки в сети и осуществить контроль потоков данных.

Ключевые слова: прогнозирование; сетевой трафик; объем; нейронечеткая сеть; гибридная система; терм; функция принадлежности; выборка; адекватность; ошибка

REFERENCES

1. Gerasina A.V. Adaptivnoye nechetkoye prognozirovaniye trafika v informatsionnykh telekommunikatsionnykh setyakh [Adaptive fuzzy prediction of traffic in information and telecommunication networks]. Systemy obrobky informatsii – Information Processing Systems, 2013, issue 9 (116), pp. 141-145.

2. Konstantinov D.V. Formuvannia adaptyvnoi tekhnolohii prymiskykh zaliznychnykh perevezen. Avtoreferat Diss. [Formation of adaptive technology of commuter rail transportation. Author’s abstract]. Kharkiv, 2010. 20 p.

3. Kostiennikov O.M. Udoskonalennia tekhnolohii formuvannia mistsevoho vahonopotoku na dilnytsi v umovakh sezonnoho kolyvannia obsiahiv navantazhennia. Avtoreferat Diss. [Improving the technology of forming a local car traffic volume at the section in terms of seasonal fluctuations in load. Author’s abstract]. Kharkiv, 2012. 20 p.

4. Leonenkov A.V. Nechetkoye modelirovaniye v srede MatLAB i fuzzy TECH [Fuzzy modeling in MatLAB and fuzzy TECH environment]. Saint-Petersburg, BKhV-Peterburg Publ., 2003. 736 p.

5. Manusov V.Z., Biryukov Ye.V. Kratkosrochnoye prognozirovaniye elektricheskoy nagruzki na osnove nechetkoy neyronnoy seti i yeye sravneniye s drugimi metodami [Short-term forecasting of electric load based on fuzzy neural network and its comparison with other methods]. Izvestiya Tomskogo politekhnicheskogo universiteta – Bulletin of the Tomsk Polytechnic University, 2006, vol. 309, no. 6, pp. 153-158.

6. Meshcheryakov V.A., Denisov I.V. Modelirovaniye adaptivnoy sistemy neyronechetkogo upravleniya rabochim protsessom strelovogo krana [Adaptive system modeling of neuro-fuzzy control of operational process for jib crane.]. Materialy V Mezhdunarodnoy nauchnoy konferentsii «Proyektirovaniye inzhenernykh i nauchnykh prilozheniy v srede MatLAB» [Proc. of V^th Intern. Sci. Conferernce «Design of Engineering and Scientific Applications in Matlab Environment»]. Kharkov, 2011, pp. 367-375.

7. Pakhomova V.M., Dmitriiev S.Yu. Rozrobka pidsystemy operatyvnoho prohnozuvannia prostoiv prybuvaiuchykh poizdiv na osnovi ANFIS-systemy [Subsystem development of operational forecasting of inactive coming trains based on ANFIS-system]. Informatsiino-keruiuchi systemy na zaliznychnomu transporti – Information and Control Systems at Railway Transport, 2013, no. 4, pp. 46-55.

8. Pakhomova V.M. Doslidzhennia inzhynirynhu trafika v kompiuternii merezhi UZ za tekhnolohiieiu MPLS TE [Research of engineering traffic in computer of Ukrzaliznytsia network using MPLS TE technology]. Nauka ta prohres transportu – Science and Transport Progress, 2015, no. 1 (55), pp. 139-147. doi: 10.15802/stp2015/3826.

9. Pokrovskaya M.A. Metod prognozirovaniya izmeneniya trafika s ispolzovaniyem neyrosetevoy modeli [Prediction method of traffic change with the use of neural network model]. T-Comm – Telekommunikatsii i Transport – T-Comm – Telecommunications and Transport, 2012, vol. 6, no. 6, pp. 27-30.

10. Rukkas K.M., Solyanik Yu.V., Ovchinnikov K.A., David O.O. Sravnitelnyy analiz metodov prognozirovaniya trafika v telekommunikatsionnykh sistemakh (Comparative analysis of traffic prediction techniques in telecommunication systems). Problemy telekommunikatsiy – Problems of Telecommunications, 2014, no. 1 (13), pp. 84-95. Available at: http://pt.journal.kh.ua/2014/1/1/141_rukkas_analysis.pdf (Accessed 22 November 2016).

11. Chabaa S., Zeroual A., Antari J. Identification and prediction of internet traffic using artificial neural networks. Journal of Intelligent Learning Systems and Applications, 2010, vol. 02, issue 03, pp. 147-155. doi: 10.4236/jilsa.2010.23018.

12. Gowrishankar S., Satyanarayana P.S. A time series modeling and prediction of wireless network traffic. Intern. Journal of Interactive Mobile Technologies (iJIM), 2009, vol. 3, issue 1, pp. 53-62. doi: 10.3991/ijim.v3i1.284.

13. Cortez P., Rio M., Rocha M., Sousa P. Multi-scale internet traffic forecasting using neural networks and time series methods. Expert Systems, 2010, vol. 29, no. 2, pp. 143-155. doi: L10.1111/j.1468-0394.2010.00568.x.

Prof. V. V. Tkachov, D. Sc. (Tech.) (Ukraine); Prof. V. V. Skalozub, D. Sc. (Tech.) (Ukraine) recommended this article to be published

Accessed: Sep. 26, 2016

Received: Dec. 05, 2016

doi © V. M. Pakhomova, 2016